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To be a multiple of 6 a number must be even and a multiple of 3.356 is not a multiple of three. The short cut to that is if the digits add up to a multiple of three then the original number is a multiple of 3.
A nonzero multiple of a number is a multiple which is not equal to 0.
There is no highest common multiple. Whatever common multiple you come up with as being their highest common multiple, I can always add their lowest common multiple (120) to get a higher common multiple.
Any multiple of 6 is a multiple of 3 and 6.
The adjective multiple should be followed by a plural noun. It would be improper to use a singular noun after the adjective multiple. Examples:I have multiple flowers in a vase.I have multiple infractions of the rules.I have multiple appointments with the dentist.